?? alleged semi-monoidal structure on co-fan category .... ??? is it really there ?? .... ???? what's it supposed to be like ???? .....

?? "categorified inf" .... ???? nullary inf as top .... ??? clearly problematic for basic opens of a toric variety .... ?? but hmmm, perhaps the categorified binary inf really does exist here .... ????? .... binary intersection of basic opens .... ???? .....

??? relationship between lax interchange transformation and "generalized day convolution as extra adjoint of essentiaql geometric morphism" .... ???? .....